Question: Find the sum: $(-39) + (-37) + \cdots + (-1)$.
Answer: The sum is an arithmetic series with common difference 2. Let $n$ be the number of terms. Then the $n$th term is $-1$, so $-39 + (n-1)(2) = -1$, or $n = 20$. The sum of an arithmetic series is equal to the average of the first and last term, multiplied by the number of terms, so the sum is $[(-39) + (-1)]/2 \cdot 20 = \boxed{-400}$.